Phase Unwrapping Problems in Digital Holographic Microscopy of Biological Cells - Biomedical Optical Phase Microscopy and Nanoscopy - page 134

rad
3.14

− 3.14

(B)

(A)

Figure 7.8
RAW cells—quality map guided flood fill unwrapping: (A) initial wrapped phase image (the areas
of discontinuous phase gradient are highlighted) and (B) unwrapped phase image. The images are
51.2 μ m 51.2 μ m (256 256 pixels).

3 3

computationally demanding, as each step requires performing one (inverse) FFT. In
practice, an “adaptive step” routine can be introduced, which will adjust the step size
depending on the phase image topology.

The slanted surface in this example can easily be reconstructed by even the simplest
software unwrapping algorithm. However, in the case when an image has a certain amount
of phase noise, even the most sophisticated algorithms still often fail in places where the 2 π

discontinuities are not closed loops [1] . Figure 7.8A shows the wrapped phase image of
several living RAW cells. As expected, the areas where the phase jumps are not continuous,
closed loops were problematic (see Figure 7.8B) . Moreover, the method clearly not only
failed in the areas where the phase jump was discontinuous (marked in Figure 7.8A) , but
the error propagated to the other parts of the image as well.

In comparison, Figure 7.9 demonstrates the results of the varying reconstruction distance
method, as it is applied to unwrap the image in Figure 7.8A . Figure 7.9A shows the first
step, where a point on the background was selected and then all the pixels with the height
of less than Δz 5 30 nm were kept. Figure 7.9B shows the removal of the areas of the

image that are not adjacent to the background area and the gray areas correspond to yet to
be unwrapped parts of the image. Figure 7.9C shows the intermediate step, where it is
already clear that the algorithm has successfully unwrapped areas that were problematic in
Figure 7.8A . Consequently, Figure 7.9D and E displays the final result using the varying
reconstruction distance method free from unwrapping errors seen in Figure 7.8 .

If a phase image, obtained from a particular reconstruction distance, is noisy in a certain area,
the images, obtained from other reconstruction distances, may not be noisy in the same area.
Thus, by varying the reconstruction distance and examining various z -planes, we can
effectively construct the unwrapped image through comparison of multiple phase images.